The Annals of Statistics

The Trimmed Mean in the Linear Model

A. H. Welsh

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Abstract

For the general linear model with independent errors, we propose and examine the large sample properties of an estimator of the regression parameter. In the location model, the estimator has the same properties as the trimmed mean and the robustness and efficiency properties of the trimmed mean carry over to the general model. The estimator depends on a preliminary estimate of the regression parameter and the residuals based on it. The properties of the adaptive estimator with data-determined trimming proportions are also investigated.

Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 20-36.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350248

Digital Object Identifier
doi:10.1214/aos/1176350248

Mathematical Reviews number (MathSciNet)
MR885722

Zentralblatt MATH identifier
0618.62074

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 60F05: Central limit and other weak theorems 62J05: Linear regression

Keywords
Adaptive estimation linear model quantiles robust estimation trimmed mean

Citation

Welsh, A. H. The Trimmed Mean in the Linear Model. Ann. Statist. 15 (1987), no. 1, 20--36. doi:10.1214/aos/1176350248. https://projecteuclid.org/euclid.aos/1176350248


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Corrections

  • See Correction: A. H. Welsh. Correction: The Trimmed Mean in the Linear Model. Ann. Statist., Volume 16, Number 1 (1988), 480--480.